421 Result(s)
within
English
Applications of Mathematics
Chapter
1996 - 1996
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Chapter and Conference Paper
Spatial Fibre and Surface Processes — Stereological Estimations and Applications
The aim of this paper is to give an introduction to the treatment of spatial fibre and surface processes especially under the aspects of modelling and stereology. In the last two decades mathematical tools wer...
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Chapter
Multiperiod-Ahead Predictive Densities and Model Comparison in Dynamic Models
This study proposes a new model comparison method which uses multiperiod-ahead predictive densities. Use of predictive densities allows us to incorporate the uncertainties associated with point forecasts in co...
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Chapter
Introduction
In the realm of symmetry various disciplines meet, resulting in a combination of knowledge that extends the abilities of each separate discipline. Publications on symmetry-related subjects are now appearing from ...
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Chapter
Introduction
At the present time many areas of science and engineering are becoming more mathematical. In this process, numerical methods play an important role. They are employed even in those areas which up to recently d...
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Chapter
Simplex Partition Strategies
The case of simplex feasible regions is common in a number of important practical applications of global optimization: examples will be discussed later, in Part 4. Typically, the simplex plays a similar role t...
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Chapter
Optimal Control of the Observation Process
This chapter is devoted to problems of the control of an observation process under various assumptions concerning the measurement matrix and the intensity of noise. A general procedure for constructing optimal...
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Chapter and Conference Paper
Least Squares Multidimensional Scaling with Transformed Distances
We consider a general least squares loss function for multidimensional scaling. Special cases of this loss function are STRESS, S-STRESS, and MULTISCALE. Several analytic results are presented. In particular, ...
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Chapter
Probability Theory
In this chapter we recapitulate some of the basic ideas and conceptions of probability theory needed to unterstand the other chapters. Though there are many text books on probability theory [2.1 – 6], a select...
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Chapter and Conference Paper
Mode Extraction by Multivalue Morphology for Cluster Analysis
The new statistical approach to unsupervised pattern classification, developed in this paper, consists to extending the multivalue morphological concepts to multidimensional functions in order to detect the mo...
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Chapter
Linear Elliptic Operators
Fundamental solutions are very useful in the theory of partial differential equations. Among many applications, they are used, e.g., in solving non-homogeneous equations like (1.4.13), and in telling us about ...
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Chapter and Conference Paper
A Theory of Wavelet Representation and Decomposition for a General Stochastic Process
Wavelets offer exciting possibilities for statistical problems. The recent paper read by Donoho et al. (1994) and the many references therein highlight some of the possibilities in a statistical context. Numerous...
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Chapter
Contribution of Electromagnetic and Gravitational Interactions into the General Solution of Ward Identities
The conformal partner of the current is the vector field A μ (x) with dimension % MathType!MTEF!2!1!+-% feaagCar...
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Chapter
Nehari manifold
Assume that φ ∈ C1(X, ℝ) is such that φ′(0) = 0. A necessary condition for u ∈ X to be a critical point of φ is that $$\langle \varphi \prime(...
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Chapter
Phase-Integral Formulas for the Regular Wave Function When There Are Turning Points Close to a Pole of the Potential
Comparison equation technique, with the Coulomb potential plus the centrifugal barrier as comparison potential, is applied to the Schrödinger equation when there are turning points close to a pole of the poten...
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Chapter and Conference Paper
Iterative Reconstruction Algorithms Based on Cross-Entropy Minimization
The “expectation maximization maximum likelihood” algorithm (EMML) has received considerable attention in the literature since its introduction in 1982 by Shepp and Vardi. A less well known algorithm, discover...
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Chapter
The Jones Revolution
In 1984, after nearly half a century in which the main focus in knot theory was the knot invariants derived from the Seifert matrix, for example, the Alexander polynomial, the signature of a knot, et cetera, V. J...
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Chapter
Orthogonalizations and Prior Distributions for Orthogonalized Model Mixing
Prediction methods based on mixing over a set of plausible models can help alleviate the sensitivity of inference and decisions to modeling assumptions. One important application area is prediction in linear m...
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Chapter and Conference Paper
Complete Heat Trace, Resolvent and Zeta Expansions for General Atiyah-Patodi-Singer Problems
The results presented in this talk were obtained jointly with R. T. Seeley in [GS1], [GS2].
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Chapter
Local Increase in the Smoothness of Generalized Solutions of Elliptic Boundry-Value Problems. Green’s Functions
In a bounded domain G ⊂ ℝ n with boundary ∂G, we consider the following elliptic boundary-value problem (4.1.1) and (4.1.2): ...
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Chapter
Miscellaneous Topics
Various topics of practical interest which relate to the previous chapters and are of applicable nature are considered. They pertain to the recent developments in the areas of poroelasticity, heat conduction a...
